“Since then,” Mr. Bernanke told his audience, “I’ve developed a view that central bankers should not try to determine fundamental values of assets.”

Indeed, Mr. Bernanke’s academic work, largely at Princeton, helped shape the conventional wisdom that central banks couldn’t spot asset bubbles and shouldn’t try to pop things that looked like bubbles. In his first speech as a Fed governor in 2002, he reiterated that trying to judge the sustainability of rapid increases in housing or stock prices was “neither desirable nor feasible.”

Over the next several years, he said repeatedly that he saw no clear evidence of a housing bubble. And in 2004, the Bernankes paid a hefty $839,000 for a town house on Capitol Hill in Washington.

It took a great recession to change his mind. The recession, prompted by the collapse of the housing bubble that Mr. Bernanke — and most other experts — failed to see coming, ended an era of minimalism in central banking. And there is no better marker than the views of Mr. Bernanke, the world’s most influential central banker, who now argues that the Fed needs to consider a range of previously unthinkable actions, including trying to pop bubbles when necessary, because sometimes the cost of doing nothing is worse.

Mr. Bernanke, who plans to step down in January after eight years as Fed chairman, will be remembered for helping to arrest the collapse of the financial system in 2008. This shy, methodical economist who had been expected to serve as the keeper of Alan Greenspan’s flame — to preserve the Fed’s hard-won success in moderating inflation — emerged under pressure as perhaps the most innovative and daring leader in the Fed’s history.

But what Mr. Bernanke did after the crisis may prove to have even more enduring influence. For almost three decades, the Fed focused on moderating inflation in the belief that this was the best and only way to help the economy. In the wake of the crisis, Mr. Bernanke forged a broader vision of the Fed’s responsibilities, starting experimental, incomplete campaigns to reduce unemployment and to prevent future crises.

The Bernanke Fed has failed to fully achieve its goals. Growth is still tepid, unemployment still too high, inflation still too low. Some critics continue to warn — so far, incorrectly — that its efforts will unleash inflation or destabilize financial markets.

Yet many of the Fed’s experiments are already being emulated by other central banks. And Mr. Bernanke’s many admirers say it is hard to imagine that anyone else could have done more under the circumstances to restore the economy. Fortunately, they say, his lifelong study of central banking under stress meant that he not only knew the available options but also understood that those options weren’t enough. And he had the credibility necessary to convince a hidebound institution to change quickly.

“It’s hard to say that the Fed has accomplished what could have or should have been accomplished,” said Michael Woodford, an economist at Columbia University. “Yet in the context of the difficulty of the challenges, the likelihood is that few other central bankers could have been as bold as Ben has been.”

Throwing Stuff at the Wall

Mr. Bernanke was a rising star at Princeton in 1994 when he persuaded 953 people to elect him to a second job — as a member of the Montgomery Township Board of Education. “I did think he was a little crazy” to add that second role, said Mark Gertler, a New York University economist who was a frequent academic collaborator with Mr. Bernanke during the 1990s.

But the move was instead an early sign of Mr. Bernanke’s restlessness with the theoretical world of academia and his nascent interest in public service. And the experience helped to prepare him for larger things.

For six years, he spent several nights a month in the library of the local high school, usually dressed in a sport coat with elbow patches, calmly contributing to heated debates about building new schools in his rapidly growing community.

“When I met him he was shy and awkward,” Professor Gertler said. “It developed his ability to moderate meetings and interact with people.”

When it comes to the sweeping overhaul of the nation’s immigration laws that Congress is considering this year, the answer is everything.

Silicon Valley executives, who have long pressed the government to provide more visas for foreign-born math and science brains, are joining forces with an array of immigration groups seeking comprehensive changes in the law. And as momentum builds in Washington for a broad revamping, the tech industry has more hope than ever that it will finally achieve its goal: the expanded access to visas that it says is critical to its own continued growth and that of the economy as a whole.

Signs of the industry’s stepped-up engagement on the issue are visible everywhere. Prominent executives met with President Obama last week. Start-up founders who rarely abandon their computers have flown across the country to meet with lawmakers.

This Tuesday, the Technology CEO Council, an advocacy organization representing companies like Dell, Intel and Motorola, had meetings on Capitol Hill. On Wednesday, Steve Case, a founder of AOL, is scheduled to testify at the first Senate hearing this year on immigration legislation, alongside the head of the deportation agents’ union and the leader of a Latino civil rights group.

“The odds of high-skilled passing without comprehensive is close to zero, and the odds of comprehensive passing without high-skilled passing is close to zero,” said Robert D. Atkinson, president of the Information Technology and Innovation Foundation, a nonpartisan research group based in Washington.

The push comes as a clutch of powerful Senate Republicans and Democrats have reached a long-elusive agreement on some basic principles of a “comprehensive” revamping of immigration law. Separately, a bipartisan bill introduced in the Senate in late January focuses directly on the visa issue.

The industry’s argument for more so-called high-skilled visas has already persuaded the president.

“Real reform means fixing the legal immigration system to cut waiting periods, reduce bureaucracy, and attract the highly-skilled entrepreneurs and engineers that will help create jobs and grow our economy,” Mr. Obama said in Tuesday’s State of the Union speech.

In a speech in Las Vegas in January in which he introduced his own blueprint for overhauling immigration law, Mr. Obama embraced the idea that granting more visas was essential to maintaining innovation and job growth. He talked about foreigners studying at American universities, figuring out how to turn their ideas into businesses.

In part, the new alliance between the tech industry and immigration groups was born out of the 2012 elections and the rising influence of Hispanic voters.

“The world has changed since the election,” said Peter J. Muller, director of government relations at Intel, pointing out that the defeat of many Republican candidates had led to a softening of the party’s position on broad changes to immigration law. “There is a focus on comprehensive. We’re thrilled by it.”

“At this point,” he added, “our best hope for immigration reform lies with comprehensive reform.”

Mr. Case, the AOL co-founder, who now runs an investment fund, echoed that sentiment after meeting with the president last Tuesday.

“I look forward to doing whatever I can to help pass comprehensive immigration reform in the months ahead,” he said, “and ensure it includes strong provisions regarding high-skilled immigration, so we are positioned to win the global battle for talent.”

That sort of sentiment delights immigrants’ rights advocates who have banged their heads against the wall for years to rally a majority of Congress around their agenda.

“The stars are aligning here,” said Ali Noorani, executive director of the National Immigration Forum. “You’ve got the politics of immigration reform changing. You’ve got tech leaders leaning in not just for high-skilled but for broader immigration reform.”

Senator Orrin G. Hatch, Republican of Utah, who is co-sponsoring the bill to increase the number of visas available for highly skilled immigrants, said the cooperation went both ways.

“All the talk about the STEM field — science, technology, engineering, mathematics — has awakened even those who aren’t all that interested in the high-tech world,” he said.

While the growing momentum has surprised many in Washington, comprehensive change is still not a sure thing, especially in the Republican-controlled House.

Mr. Hatch said he would push forward with his measure even if the broader efforts foundered. But his Democratic co-sponsor, Amy Klobuchar of Minnesota, said she would press for the bill to be part of the comprehensive package.

Last year, technology executives had a taste of what could happen with stand-alone legislation.

Pessimism mounted among members of the committee about their ability to strike a deal by Monday and avert a high-profile failure that would demonstrate anew the inability of the two parties on Capitol Hill to reach consensus about how to attack the nation’s mounting public debt. The partisan divide was also showcased Friday by a vote in the House to reject a Republican-backed constitutional amendment requiring a balanced federal budget.

Despite time running out on the committee created by the summer agreement to raise the federal debt limit, negotiations were in disarray, with Republicans and Democrats even disputing what precisely divided them. One panel member said that he still had slim hope for a deal but that it would take an extraordinary development to end the stalemate and avoid a series of automatic cuts in 2013 that would reduce federal services and make substantial reductions in Pentagon spending.

Seeking to reach at least a partial accord, Republicans made their six Democratic counterparts on the committee an offer that would get to roughly half of its goal — a retreat for an earlier plan with cuts in spending and revenue increases — but Democrats rejected it out of hand as inadequate. Democrats said the proposal was unbalanced because it was overly dependent on spending cuts with only a small amount of new revenue.

“If they maintain this,” said Representative James E. Clyburn of South Carolina, a Democratic member of the committee, in an interview, “then this is not going to happen.” Mr. Boehner, stepping in to the talks as the deadline neared, helped devise the Republican proposal, which offered less in new revenues than a previous Republican plan. But Republicans said the proposal also would not touch Medicare, Medicaid or Social Security, so they said they were surprised it was spurned. Mr. Boehner left town on Friday pessimistic that a deal could be made by the Monday evening deadline, his aides said.

“This was a balanced, bipartisan plan,” said Kevin Smith, a spokesman for Mr. Boehner. “The fact that it was rejected makes it clear that Washington Democrats won’t cut a dime in government spending without job-killing tax hikes.”

Senator John Kerry, Democrat of Massachusetts and a member of the committee, said in an interview that he still had hope, but that “we’re really having a hard time bringing our colleagues to what is fair, what is balanced.”

Aides to lawmakers in both parties, speaking anonymously because they did not want to be seen as sabotaging the negotiations, were even more negative. “I do not feel any last-minute sense of urgency,” one said.

The group has until Monday to submit a plan to the Congressional Budget Office for evaluation before presenting it to the full Congress on Wednesday, leaving time for reaching the sort of last-minute breakthrough that often occurs on Capitol Hill when lawmakers face a deadline. But members said the divisions were so deep, and good will so lacking, that their expectations were eroding.

The divide was further illustrated by the House’s rejection of a constitutional amendment that would generally require the federal government to balance its budget. The House voted 261 to 165 in favor of the proposal, but that was 23 votes short of the two-thirds majority needed to advance a constitutional amendment. The vast majority of Republicans supported the measure. Democrats, even some who voted in favor of a similar measure in 1995, pushed it to failure.

The dynamic Friday mirrored that of other high-stakes fiscal fights in the 112th Congress, like the brawl last summer over legislation to lift the debt ceiling and avoid default and a fight over a spending measure that was also resolved within hours of a government shutdown. But without an immediate threat of fiscal calamity, as was the case in both those instances, the cuts to federal spending triggered by a committee failure would not take place until 2013, leaving Congress an opportunity to find other escape hatches.

Republicans and Democrats provided radically different descriptions of the Republicans’ latest offer, intended to reduce budget deficits by $643 billion over 10 years. Republicans said their proposal called for $229 billion in new revenue and fees, including taxes on owners of corporate jets, and $316 billion in cuts in spending, including $100 billion from the Defense Department. Republicans said these cuts would reduce the need for federal borrowing and thus reduce interest payments on the federal debt by $100 billion over 10 years.

Democrats said the amount of tax revenue in the Republicans’ plan — $3 billion from owners of corporate jets — was laughable.

Central to the impasse is a fundamental disagreement over how much revenue would be raised toward the $1.2 trillion, and what the role of the Bush-era tax cuts, which are set to expire at the end of next year, would play. Republicans want to maintain the cuts; Democrats want them eliminated for the nation’s highest earners.

Most members of the committee intend to stay in town over the weekend and continue talking. Half the members are scheduled to appear on the Sunday morning television talk shows, where they will almost certainly have to discuss whether their efforts are doomed. Members of the panel are trying to figure out how to manage the denouement of the panel’s narrative, which began with their first meeting 10 weeks ago.

One option is for the panel to meet and vote next week on deficit reduction plans devised by the two parties. However, Congressional leaders are cool to that idea, saying it makes no sense to have the public embarrassment of a meeting that would showcase a failure to solve some of the nation’s biggest problems.

We’ve just published an interview with Neil Blumenthal, a young entrepreneur who recently went to Capitol Hill to talk about how important young entrepreneurs are to the economy. One of the founders of Warby Parker, an online eyewear company based in New York, Mr. Blumenthal and Hannah Seligson discussed, among other things, what politicians don’t understand about business, what he had to promise the Small Business Administration he wouldn’t do with his borrowed money, and what the Bloomberg administration is doing right. (You can read more small-business conversations here.)

At one point, Mr. Blumenthal noted that his company had struggled to get a loan backed by the Small Business Administration because the company did not yet have two years of tax returns.

“Isn’t that a reasonable request when you’re talking about using taxpayer dollars to guarantee a loan to a private company?” Ms. Seligson asked.

“I understand where the banks are coming from,” Mr. Blumenthal responded. “It probably was necessary to implement hard and fast rules to stop the bleeding when the crisis hit, but they should be looking at the policies and thinking: does this make sense now?”

Despite a day of frenzied legislative maneuvering and another attempt by President Obama to rally public opinion behind some kind of compromise, the two parties made no visible progress in finding common ground, leaving Washington, Wall Street and much of the nation watching the clock toward a deadline of midnight Tuesday.

Demonstrating the deep partisan divide coloring the budget fight, the House voted 218 to 210 to approve the plan endorsed by Speaker John A. Boehner to increase the federal debt ceiling in two stages. No Democrats supported the measure; 22 Republicans opposed it. The White House condemned it as a “political exercise.”

“To the American people, I would say we tried our level best,” Mr. Boehner said as he concluded a debate that had been abruptly halted Thursday evening when he fell short of the votes for victory. “We tried to do our best for our country, but some people still say no.”

The House vote was the first act of what loomed as a weekend of tense legislative gamesmanship on Capitol Hill. With Congressional leaders still unable to reach agreement, anxious lawmakers, aides and administration officials seemed to hold their breath, hoping that some compromise could mesh the competing proposals and rise above the increasingly confrontational tactics in Washington.

Aides and lawmakers said back-channel talks across the aisle were not making much progress in the Senate, but they hoped the pace would pick up after the Senate rejection of the House proposal.

That did not take long. Two hours after the House approved its plan, it was convincingly tabled in the Senate by a vote of 59 to 41, and Democrats took steps to move ahead with their proposal.

In an effort to attract some Republican support for his plan, Mr. Reid made a number of changes in his bill. But the Congressional Budget Office found that the overall impact on the deficit was about the same as with his original bill: savings of $2.2 trillion over 10 years.

House Republicans, stung by their inability on Thursday to secure enough votes from conservatives for their own plan to raise the debt ceiling, reconfigured their proposal to win over the holdouts.

The revised plan would raise the debt ceiling for about six months in exchange for $1 trillion in spending cuts. A second installment of $1.6 trillion — expected to be needed in about six months — would hinge on Congressional approval of a constitutional amendment requiring a balanced budget, a provision added Friday to lure conservatives.

But the revisions only made the measure less acceptable to Senate Democrats, who had made it clear that they would reject the bill as soon as it reached them. “This is the most outrageous suggestion I have heard,” said Senator Richard J. Durbin, the assistant Democratic leader.

Though Mr. Boehner and his allies had secured the votes, the margin of victory was narrow. Lawmakers, aware that the fight was probably not over, did not celebrate with the usual applause, hooping and hollering that erupts when a hard-fought bill goes over the top.

Indeed, an eerie silence settled over the House chamber. Republicans had won, but were in no mood to cheer the prospect of a $2.5 trillion increase in the federal debt limit, a possible fight with the Senate or a default.

Earlier in the day at the White House, Mr. Obama said “any solution to avoid default must be bipartisan. I urge Democrats and Republicans in the Senate to find common ground on a plan that can get support from both parties in the House, a plan that I can sign by Tuesday.”

Mr. Obama urged Republicans in the House and Senate to abandon a bill that “does not solve the problem” and has no chance of passage in the Senate. “There are a lot of crises in the world that we can’t always predict or avoid,” he said. “This isn’t one of those crises.”

In an effort to send a message, House Republicans plan to allow a symbolic vote Saturday on Mr. Reid’s plan to show that it cannot clear the House.